Black holes collide in the best simulation yet

The ripples in space-time created when two black holes merge have been modelled to unprecedented accuracy, according to Einstein's equations, by a powerful new computer simulation. The "waveform" signatures produced in the simulation should help researchers identify the ripples in the data from gravitational wave detectors.

Powerful gravitational waves are thought to shake the fabric of space-time when two black holes spiral towards each other and eventually merge. The waves have not yet been observed, but researchers have been trying to simulate the process on computers in order to predict the expected signal. That will help the nascent searches now in progress.

The signals, called "waveforms", are shaped by factors such as the frequency at which the two black holes orbit each other, their relative masses and their spins. But modelling the merger has proven exceptionally difficult because the process is governed by Einstein's theory of general relativity.

"People have been trying for years to follow the coalescence of two black holes where you treat general relativity exactly," comments David Merritt, an astrophysicist at the Rochester Institute of Technology in New York, US.

John Baker of NASA's Goddard Space Flight Center in Greenbelt, Maryland, US, agrees. "Part of the complexity of simulating Einstein's equations are the equations don't come in a unique form," he told New Scientist. "You have a lot of choices to make when you approach the problem."

Gridlock

Some of these choices lead computers to crash because the grid-like system that describes space-time becomes "all twisted up because the grid lines fall on top of each other", says Baker.

But several groups - including Baker's - have recently come up with ways to choose coordinate systems that do not become tangled. Now, he and his colleagues have performed the longest simulation of a black hole merger that has consistently returned the same waveforms. "It really demonstrates it is the right answer," he says.

The simulation followed two non-spinning black holes of equal mass that orbited each other between 1.5 and 4.5 times before merging. For black holes about 500,000 times the mass of the Sun, this final death spiral is expected to take just an hour or so, but the simulations required several days of computation time by 2000 individual processors at NASA's Columbia supercomputer in California, US. View an mpeg video of the simulation here.

"The simulations start out with the black holes practically touching because it's such an expensive calculation," says Merritt. And the simulations represent a simplified case - most black holes are thought to spin and binary systems should have black holes of different masses. But they will still be useful, he says.

Noisy data

Pairs of orbiting black holes can be described by just 10 or so key numbers - including their mass, spin, and the direction of their spin, he says. If researchers simulate all the possible permutations of those numbers, they will get "templates" for each scenario, he says.

"It's hard to detect gravitational waves," Merritt told New Scientist. "So if you think you know what a waveform looks like, you could use that as a template to filter out your noisy data."

Large black holes that orbit each other relatively slowly before colliding could be detected by space-based observatories, such as the proposed LISA (Laser Interferometer Space Antenna), Baker says. That is because these low-frequency waves require a very large detector to be picked up, and LISA's three spacecraft would orbit the Sun 5 million kilometres apart.

Smaller black holes, however, orbit each other 100,000 times more quickly before merging, so they produce higher frequency gravitational waves. These waves could be picked up by smaller, ground-based detectors such as the US-based LIGO (Laser Interferometer Gravitational-Wave Observatory). LIGO uses twin L-shaped detectors, each 4 kilometres long, in Washington state and Louisiana, US.

Journal reference: Physical Review Letters (vol 96, no 111102)

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